LMFDB - Embedded newform 5054.2.a.bj.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5054,2,Mod(1,5054)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5054, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("5054.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5054 = 2 \cdot 7 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5054.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$40.3563931816$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 3x^{8} - 15x^{7} + 40x^{6} + 81x^{5} - 162x^{4} - 205x^{3} + 204x^{2} + 210x + 1 $ x^9 - 3x^8 - 15x^7 + 40x^6 + 81x^5 - 162x^4 - 205x^3 + 204x^2 + 210x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 266)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-0.00478425$ of defining polynomial
Character	$\chi$	$=$	5054.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.00478425 q^{3} +1.00000 q^{4} -1.04022 q^{5} -0.00478425 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.99998 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.00478425 q^{3} +1.00000 q^{4} -1.04022 q^{5} -0.00478425 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.99998 q^{9} +1.04022 q^{10} -4.80065 q^{11} +0.00478425 q^{12} -3.58726 q^{13} +1.00000 q^{14} -0.00497667 q^{15} +1.00000 q^{16} -6.75875 q^{17} +2.99998 q^{18} -1.04022 q^{20} -0.00478425 q^{21} +4.80065 q^{22} +0.904993 q^{23} -0.00478425 q^{24} -3.91794 q^{25} +3.58726 q^{26} -0.0287054 q^{27} -1.00000 q^{28} -3.14529 q^{29} +0.00497667 q^{30} -2.02562 q^{31} -1.00000 q^{32} -0.0229675 q^{33} +6.75875 q^{34} +1.04022 q^{35} -2.99998 q^{36} -9.28058 q^{37} -0.0171623 q^{39} +1.04022 q^{40} -8.12230 q^{41} +0.00478425 q^{42} +10.7453 q^{43} -4.80065 q^{44} +3.12063 q^{45} -0.904993 q^{46} +8.48256 q^{47} +0.00478425 q^{48} +1.00000 q^{49} +3.91794 q^{50} -0.0323355 q^{51} -3.58726 q^{52} -8.76649 q^{53} +0.0287054 q^{54} +4.99373 q^{55} +1.00000 q^{56} +3.14529 q^{58} +1.50504 q^{59} -0.00497667 q^{60} -10.5597 q^{61} +2.02562 q^{62} +2.99998 q^{63} +1.00000 q^{64} +3.73154 q^{65} +0.0229675 q^{66} -8.96291 q^{67} -6.75875 q^{68} +0.00432971 q^{69} -1.04022 q^{70} -8.59288 q^{71} +2.99998 q^{72} +13.5766 q^{73} +9.28058 q^{74} -0.0187444 q^{75} +4.80065 q^{77} +0.0171623 q^{78} +14.4598 q^{79} -1.04022 q^{80} +8.99979 q^{81} +8.12230 q^{82} +0.247904 q^{83} -0.00478425 q^{84} +7.03058 q^{85} -10.7453 q^{86} -0.0150478 q^{87} +4.80065 q^{88} -3.50543 q^{89} -3.12063 q^{90} +3.58726 q^{91} +0.904993 q^{92} -0.00969106 q^{93} -8.48256 q^{94} -0.00478425 q^{96} -15.6407 q^{97} -1.00000 q^{98} +14.4018 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 9 q^{2} - 3 q^{3} + 9 q^{4} + 3 q^{5} + 3 q^{6} - 9 q^{7} - 9 q^{8} + 12 q^{9}+O(q^{10}) $ 9 * q - 9 * q^2 - 3 * q^3 + 9 * q^4 + 3 * q^5 + 3 * q^6 - 9 * q^7 - 9 * q^8 + 12 * q^9	\( 9 q - 9 q^{2} - 3 q^{3} + 9 q^{4} + 3 q^{5} + 3 q^{6} - 9 q^{7} - 9 q^{8} + 12 q^{9} - 3 q^{10} - 3 q^{11} - 3 q^{12} - 12 q^{13} + 9 q^{14} + 6 q^{15} + 9 q^{16} + 12 q^{17} - 12 q^{18} + 3 q^{20} + 3 q^{21} + 3 q^{22} + 6 q^{23} + 3 q^{24} + 12 q^{26} - 24 q^{27} - 9 q^{28} + 6 q^{29} - 6 q^{30} - 9 q^{31} - 9 q^{32} + 3 q^{33} - 12 q^{34} - 3 q^{35} + 12 q^{36} - 9 q^{37} + 33 q^{39} - 3 q^{40} - 3 q^{41} - 3 q^{42} + 21 q^{43} - 3 q^{44} + 18 q^{45} - 6 q^{46} + 21 q^{47} - 3 q^{48} + 9 q^{49} - 39 q^{51} - 12 q^{52} + 24 q^{54} + 24 q^{55} + 9 q^{56} - 6 q^{58} + 9 q^{59} + 6 q^{60} + 6 q^{61} + 9 q^{62} - 12 q^{63} + 9 q^{64} + 3 q^{65} - 3 q^{66} - 27 q^{67} + 12 q^{68} - 6 q^{69} + 3 q^{70} - 9 q^{71} - 12 q^{72} + 51 q^{73} + 9 q^{74} + 3 q^{75} + 3 q^{77} - 33 q^{78} - 24 q^{79} + 3 q^{80} - 3 q^{81} + 3 q^{82} + 9 q^{83} + 3 q^{84} + 6 q^{85} - 21 q^{86} - 3 q^{87} + 3 q^{88} - 9 q^{89} - 18 q^{90} + 12 q^{91} + 6 q^{92} + 3 q^{93} - 21 q^{94} + 3 q^{96} + 12 q^{97} - 9 q^{98} - 15 q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 - 3 * q^3 + 9 * q^4 + 3 * q^5 + 3 * q^6 - 9 * q^7 - 9 * q^8 + 12 * q^9 - 3 * q^10 - 3 * q^11 - 3 * q^12 - 12 * q^13 + 9 * q^14 + 6 * q^15 + 9 * q^16 + 12 * q^17 - 12 * q^18 + 3 * q^20 + 3 * q^21 + 3 * q^22 + 6 * q^23 + 3 * q^24 + 12 * q^26 - 24 * q^27 - 9 * q^28 + 6 * q^29 - 6 * q^30 - 9 * q^31 - 9 * q^32 + 3 * q^33 - 12 * q^34 - 3 * q^35 + 12 * q^36 - 9 * q^37 + 33 * q^39 - 3 * q^40 - 3 * q^41 - 3 * q^42 + 21 * q^43 - 3 * q^44 + 18 * q^45 - 6 * q^46 + 21 * q^47 - 3 * q^48 + 9 * q^49 - 39 * q^51 - 12 * q^52 + 24 * q^54 + 24 * q^55 + 9 * q^56 - 6 * q^58 + 9 * q^59 + 6 * q^60 + 6 * q^61 + 9 * q^62 - 12 * q^63 + 9 * q^64 + 3 * q^65 - 3 * q^66 - 27 * q^67 + 12 * q^68 - 6 * q^69 + 3 * q^70 - 9 * q^71 - 12 * q^72 + 51 * q^73 + 9 * q^74 + 3 * q^75 + 3 * q^77 - 33 * q^78 - 24 * q^79 + 3 * q^80 - 3 * q^81 + 3 * q^82 + 9 * q^83 + 3 * q^84 + 6 * q^85 - 21 * q^86 - 3 * q^87 + 3 * q^88 - 9 * q^89 - 18 * q^90 + 12 * q^91 + 6 * q^92 + 3 * q^93 - 21 * q^94 + 3 * q^96 + 12 * q^97 - 9 * q^98 - 15 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	0.00478425	0.00276219	0.00138109	−	0.999999i	$-0.499560\pi$
$3$	0.00478425	0.00276219	0.00138109	+	0.999999i	$0.499560\pi$
$4$	1.00000	0.500000
$5$	−1.04022	−0.465200	−0.232600	−	0.972572i	$-0.574723\pi$
$5$	−1.04022	−0.465200	−0.232600	+	0.972572i	$0.574723\pi$
$6$	−0.00478425	−0.00195316
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	−2.99998	−0.999992
$10$	1.04022	0.328946
$11$	−4.80065	−1.44745	−0.723725	−	0.690088i	$-0.757572\pi$
$11$	−4.80065	−1.44745	−0.723725	+	0.690088i	$0.757572\pi$
$12$	0.00478425	0.00138109
$13$	−3.58726	−0.994928	−0.497464	−	0.867485i	$-0.665735\pi$
$13$	−3.58726	−0.994928	−0.497464	+	0.867485i	$0.665735\pi$
$14$	1.00000	0.267261
$15$	−0.00497667	−0.00128497
$16$	1.00000	0.250000
$17$	−6.75875	−1.63924	−0.819619	−	0.572910i	$-0.805815\pi$
$17$	−6.75875	−1.63924	−0.819619	+	0.572910i	$0.805815\pi$
$18$	2.99998	0.707101
$19$	0	0
$19$	0	0
$20$	−1.04022	−0.232600
$21$	−0.00478425	−0.00104401
$22$	4.80065	1.02350
$23$	0.904993	0.188704	0.0943520	−	0.995539i	$-0.469922\pi$
$23$	0.904993	0.188704	0.0943520	+	0.995539i	$0.469922\pi$
$24$	−0.00478425	−0.000976580 0
$25$	−3.91794	−0.783589
$26$	3.58726	0.703520
$27$	−0.0287054	−0.00552435
$28$	−1.00000	−0.188982
$29$	−3.14529	−0.584065	−0.292033	−	0.956408i	$-0.594332\pi$
$29$	−3.14529	−0.584065	−0.292033	+	0.956408i	$0.594332\pi$
$30$	0.00497667	0.000908611 0
$31$	−2.02562	−0.363812	−0.181906	−	0.983316i	$-0.558227\pi$
$31$	−2.02562	−0.363812	−0.181906	+	0.983316i	$0.558227\pi$
$32$	−1.00000	−0.176777
$33$	−0.0229675	−0.00399813
$34$	6.75875	1.15912
$35$	1.04022	0.175829
$36$	−2.99998	−0.499996
$37$	−9.28058	−1.52572	−0.762859	−	0.646564i	$-0.776205\pi$
$37$	−9.28058	−1.52572	−0.762859	+	0.646564i	$0.776205\pi$
$38$	0	0
$39$	−0.0171623	−0.00274818
$40$	1.04022	0.164473
$41$	−8.12230	−1.26849	−0.634245	−	0.773132i	$-0.718689\pi$
$41$	−8.12230	−1.26849	−0.634245	+	0.773132i	$0.718689\pi$
$42$	0.00478425	0.000738225 0
$43$	10.7453	1.63865	0.819325	−	0.573329i	$-0.194348\pi$
$43$	10.7453	1.63865	0.819325	+	0.573329i	$0.194348\pi$
$44$	−4.80065	−0.723725
$45$	3.12063	0.465197
$46$	−0.904993	−0.133434
$47$	8.48256	1.23731	0.618654	−	0.785663i	$-0.287678\pi$
$47$	8.48256	1.23731	0.618654	+	0.785663i	$0.287678\pi$
$48$	0.00478425	0.000690546 0
$49$	1.00000	0.142857
$50$	3.91794	0.554081
$51$	−0.0323355	−0.00452788
$52$	−3.58726	−0.497464
$53$	−8.76649	−1.20417	−0.602085	−	0.798432i	$-0.705663\pi$
$53$	−8.76649	−1.20417	−0.602085	+	0.798432i	$0.705663\pi$
$54$	0.0287054	0.00390631
$55$	4.99373	0.673355
$56$	1.00000	0.133631
$57$	0	0
$58$	3.14529	0.412997
$59$	1.50504	0.195939	0.0979697	−	0.995189i	$-0.468765\pi$
$59$	1.50504	0.195939	0.0979697	+	0.995189i	$0.468765\pi$
$60$	−0.00497667	−0.000642485 0
$61$	−10.5597	−1.35203	−0.676017	−	0.736886i	$-0.736295\pi$
$61$	−10.5597	−1.35203	−0.676017	+	0.736886i	$0.736295\pi$
$62$	2.02562	0.257254
$63$	2.99998	0.377962
$64$	1.00000	0.125000
$65$	3.73154	0.462841
$66$	0.0229675	0.00282710
$67$	−8.96291	−1.09499	−0.547497	−	0.836808i	$-0.684419\pi$
$67$	−8.96291	−1.09499	−0.547497	+	0.836808i	$0.684419\pi$
$68$	−6.75875	−0.819619
$69$	0.00432971	0.000521236 0
$70$	−1.04022	−0.124330
$71$	−8.59288	−1.01979	−0.509893	−	0.860238i	$-0.670315\pi$
$71$	−8.59288	−1.01979	−0.509893	+	0.860238i	$0.670315\pi$
$72$	2.99998	0.353551
$73$	13.5766	1.58903	0.794513	−	0.607247i	$-0.207726\pi$
$73$	13.5766	1.58903	0.794513	+	0.607247i	$0.207726\pi$
$74$	9.28058	1.07885
$75$	−0.0187444	−0.00216442
$76$	0	0
$77$	4.80065	0.547085
$78$	0.0171623	0.00194325
$79$	14.4598	1.62685	0.813426	−	0.581668i	$-0.197600\pi$
$79$	14.4598	1.62685	0.813426	+	0.581668i	$0.197600\pi$
$80$	−1.04022	−0.116300
$81$	8.99979	0.999977
$82$	8.12230	0.896958
$83$	0.247904	0.0272110	0.0136055	−	0.999907i	$-0.495669\pi$
$83$	0.247904	0.0272110	0.0136055	+	0.999907i	$0.495669\pi$
$84$	−0.00478425	−0.000522004 0
$85$	7.03058	0.762574
$86$	−10.7453	−1.15870
$87$	−0.0150478	−0.00161330
$88$	4.80065	0.511751
$89$	−3.50543	−0.371575	−0.185787	−	0.982590i	$-0.559484\pi$
$89$	−3.50543	−0.371575	−0.185787	+	0.982590i	$0.559484\pi$
$90$	−3.12063	−0.328944
$91$	3.58726	0.376047
$92$	0.904993	0.0943520
$93$	−0.00969106	−0.00100492
$94$	−8.48256	−0.874909
$95$	0	0
$96$	−0.00478425	−0.000488290 0
$97$	−15.6407	−1.58808	−0.794038	−	0.607868i	$-0.792025\pi$
$97$	−15.6407	−1.58808	−0.794038	+	0.607868i	$0.792025\pi$
$98$	−1.00000	−0.101015
$99$	14.4018	1.44744
$100$	−3.91794	−0.391794
$101$	−16.2551	−1.61744	−0.808721	−	0.588193i	$-0.799840\pi$
$101$	−16.2551	−1.61744	−0.808721	+	0.588193i	$0.799840\pi$
$102$	0.0323355	0.00320169
$103$	11.1490	1.09854	0.549271	−	0.835644i	$-0.314905\pi$
$103$	11.1490	1.09854	0.549271	+	0.835644i	$0.314905\pi$
$104$	3.58726	0.351760
$105$	0.00497667	0.000485673 0
$106$	8.76649	0.851477
$107$	4.43719	0.428959	0.214480	−	0.976728i	$-0.431194\pi$
$107$	4.43719	0.428959	0.214480	+	0.976728i	$0.431194\pi$
$108$	−0.0287054	−0.00276218
$109$	10.2070	0.977656	0.488828	−	0.872380i	$-0.337425\pi$
$109$	10.2070	0.977656	0.488828	+	0.872380i	$0.337425\pi$
$110$	−4.99373	−0.476134
$111$	−0.0444006	−0.00421432
$112$	−1.00000	−0.0944911
$113$	16.8296	1.58319	0.791596	−	0.611045i	$-0.209251\pi$
$113$	16.8296	1.58319	0.791596	+	0.611045i	$0.209251\pi$
$114$	0	0
$115$	−0.941391	−0.0877852
$116$	−3.14529	−0.292033
$117$	10.7617	0.994920
$118$	−1.50504	−0.138550
$119$	6.75875	0.619573
$120$	0.00497667	0.000454305 0
$121$	12.0463	1.09511
$122$	10.5597	0.956033
$123$	−0.0388591	−0.00350380
$124$	−2.02562	−0.181906
$125$	9.27662	0.829726
$126$	−2.99998	−0.267259
$127$	−16.0991	−1.42857	−0.714284	−	0.699856i	$-0.753247\pi$
$127$	−16.0991	−1.42857	−0.714284	+	0.699856i	$0.753247\pi$
$128$	−1.00000	−0.0883883
$129$	0.0514084	0.00452626
$130$	−3.73154	−0.327278
$131$	0.113488	0.00991550	0.00495775	−	0.999988i	$-0.498422\pi$
$131$	0.113488	0.00991550	0.00495775	+	0.999988i	$0.498422\pi$
$132$	−0.0229675	−0.00199906
$133$	0	0
$134$	8.96291	0.774278
$135$	0.0298599	0.00256993
$136$	6.75875	0.579558
$137$	−7.33889	−0.627003	−0.313502	−	0.949588i	$-0.601502\pi$
$137$	−7.33889	−0.627003	−0.313502	+	0.949588i	$0.601502\pi$
$138$	−0.00432971	−0.000368569 0
$139$	−0.503371	−0.0426954	−0.0213477	−	0.999772i	$-0.506796\pi$
$139$	−0.503371	−0.0426954	−0.0213477	+	0.999772i	$0.506796\pi$
$140$	1.04022	0.0879146
$141$	0.0405827	0.00341768
$142$	8.59288	0.721098
$143$	17.2212	1.44011
$144$	−2.99998	−0.249998
$145$	3.27179	0.271707
$146$	−13.5766	−1.12361
$147$	0.00478425	0.000394598 0
$148$	−9.28058	−0.762859
$149$	−3.06660	−0.251226	−0.125613	−	0.992079i	$-0.540090\pi$
$149$	−3.06660	−0.251226	−0.125613	+	0.992079i	$0.540090\pi$
$150$	0.0187444	0.00153047
$151$	8.09348	0.658638	0.329319	−	0.944219i	$-0.393181\pi$
$151$	8.09348	0.658638	0.329319	+	0.944219i	$0.393181\pi$
$152$	0	0
$153$	20.2761	1.63922
$154$	−4.80065	−0.386848
$155$	2.10709	0.169245
$156$	−0.0171623	−0.00137409
$157$	10.6799	0.852349	0.426175	−	0.904641i	$-0.359861\pi$
$157$	10.6799	0.852349	0.426175	+	0.904641i	$0.359861\pi$
$158$	−14.4598	−1.15036
$159$	−0.0419411	−0.00332614
$160$	1.04022	0.0822366
$161$	−0.904993	−0.0713234
$162$	−8.99979	−0.707091
$163$	−16.2677	−1.27419	−0.637093	−	0.770787i	$-0.719863\pi$
$163$	−16.2677	−1.27419	−0.637093	+	0.770787i	$0.719863\pi$
$164$	−8.12230	−0.634245
$165$	0.0238912	0.00185993
$166$	−0.247904	−0.0192411
$167$	−15.2244	−1.17810	−0.589050	−	0.808097i	$-0.700498\pi$
$167$	−15.2244	−1.17810	−0.589050	+	0.808097i	$0.700498\pi$
$168$	0.00478425	0.000369113 0
$169$	−0.131544	−0.0101188
$170$	−7.03058	−0.539221
$171$	0	0
$172$	10.7453	0.819325
$173$	−0.0992419	−0.00754523	−0.00377261	−	0.999993i	$-0.501201\pi$
$173$	−0.0992419	−0.00754523	−0.00377261	+	0.999993i	$0.501201\pi$
$174$	0.0150478	0.00114077
$175$	3.91794	0.296169
$176$	−4.80065	−0.361863
$177$	0.00720048	0.000541221 0
$178$	3.50543	0.262743
$179$	−3.77228	−0.281953	−0.140977	−	0.990013i	$-0.545024\pi$
$179$	−3.77228	−0.281953	−0.140977	+	0.990013i	$0.545024\pi$
$180$	3.12063	0.232598
$181$	11.1776	0.830826	0.415413	−	0.909633i	$-0.363637\pi$
$181$	11.1776	0.830826	0.415413	+	0.909633i	$0.363637\pi$
$182$	−3.58726	−0.265906
$183$	−0.0505203	−0.00373457
$184$	−0.904993	−0.0667170
$185$	9.65385	0.709765
$186$	0.00969106	0.000710583 0
$187$	32.4464	2.37272
$188$	8.48256	0.618654
$189$	0.0287054	0.00208801
$190$	0	0
$191$	6.03722	0.436838	0.218419	−	0.975855i	$-0.429910\pi$
$191$	6.03722	0.436838	0.218419	+	0.975855i	$0.429910\pi$
$192$	0.00478425	0.000345273 0
$193$	−19.2872	−1.38833	−0.694163	−	0.719818i	$-0.744225\pi$
$193$	−19.2872	−1.38833	−0.694163	+	0.719818i	$0.744225\pi$
$194$	15.6407	1.12294
$195$	0.0178526	0.00127845
$196$	1.00000	0.0714286
$197$	−7.25265	−0.516730	−0.258365	−	0.966047i	$-0.583184\pi$
$197$	−7.25265	−0.516730	−0.258365	+	0.966047i	$0.583184\pi$
$198$	−14.4018	−1.02349
$199$	11.0987	0.786766	0.393383	−	0.919375i	$-0.371305\pi$
$199$	11.0987	0.786766	0.393383	+	0.919375i	$0.371305\pi$
$200$	3.91794	0.277040
$201$	−0.0428808	−0.00302458
$202$	16.2551	1.14370
$203$	3.14529	0.220756
$204$	−0.0323355	−0.00226394
$205$	8.44897	0.590102
$206$	−11.1490	−0.776787
$207$	−2.71496	−0.188703
$208$	−3.58726	−0.248732
$209$	0	0
$210$	−0.00497667	−0.000343423 0
$211$	−11.5491	−0.795070	−0.397535	−	0.917587i	$-0.630134\pi$
$211$	−11.5491	−0.795070	−0.397535	+	0.917587i	$0.630134\pi$
$212$	−8.76649	−0.602085
$213$	−0.0411104	−0.00281684
$214$	−4.43719	−0.303320
$215$	−11.1775	−0.762301
$216$	0.0287054	0.00195315
$217$	2.02562	0.137508
$218$	−10.2070	−0.691307
$219$	0.0649540	0.00438919
$220$	4.99373	0.336677
$221$	24.2454	1.63092
$222$	0.0444006	0.00297997
$223$	−11.9313	−0.798981	−0.399491	−	0.916737i	$-0.630813\pi$
$223$	−11.9313	−0.798981	−0.399491	+	0.916737i	$0.630813\pi$
$224$	1.00000	0.0668153
$225$	11.7537	0.783583
$226$	−16.8296	−1.11949
$227$	−14.7425	−0.978496	−0.489248	−	0.872145i	$-0.662729\pi$
$227$	−14.7425	−0.978496	−0.489248	+	0.872145i	$0.662729\pi$
$228$	0	0
$229$	−5.04641	−0.333476	−0.166738	−	0.986001i	$-0.553323\pi$
$229$	−5.04641	−0.333476	−0.166738	+	0.986001i	$0.553323\pi$
$230$	0.941391	0.0620735
$231$	0.0229675	0.00151115
$232$	3.14529	0.206498
$233$	5.11488	0.335087	0.167543	−	0.985865i	$-0.446417\pi$
$233$	5.11488	0.335087	0.167543	+	0.985865i	$0.446417\pi$
$234$	−10.7617	−0.703515
$235$	−8.82373	−0.575596
$236$	1.50504	0.0979697
$237$	0.0691791	0.00449367
$238$	−6.75875	−0.438105
$239$	−21.8093	−1.41072	−0.705362	−	0.708847i	$-0.749216\pi$
$239$	−21.8093	−1.41072	−0.705362	+	0.708847i	$0.749216\pi$
$240$	−0.00497667	−0.000321242 0
$241$	−1.76058	−0.113409	−0.0567044	−	0.998391i	$-0.518059\pi$
$241$	−1.76058	−0.113409	−0.0567044	+	0.998391i	$0.518059\pi$
$242$	−12.0463	−0.774363
$243$	0.129173	0.00828647
$244$	−10.5597	−0.676017
$245$	−1.04022	−0.0664572
$246$	0.0388591	0.00247756
$247$	0	0
$248$	2.02562	0.128627
$249$	0.00118604	7.51620e−5 0
$250$	−9.27662	−0.586705
$251$	−16.8967	−1.06651	−0.533256	−	0.845954i	$-0.679032\pi$
$251$	−16.8967	−1.06651	−0.533256	+	0.845954i	$0.679032\pi$
$252$	2.99998	0.188981
$253$	−4.34456	−0.273140
$254$	16.0991	1.01015
$255$	0.0336360	0.00210637
$256$	1.00000	0.0625000
$257$	−8.77380	−0.547295	−0.273647	−	0.961830i	$-0.588230\pi$
$257$	−8.77380	−0.547295	−0.273647	+	0.961830i	$0.588230\pi$
$258$	−0.0514084	−0.00320055
$259$	9.28058	0.576667
$260$	3.73154	0.231420
$261$	9.43579	0.584061
$262$	−0.113488	−0.00701132
$263$	−10.1046	−0.623075	−0.311538	−	0.950234i	$-0.600844\pi$
$263$	−10.1046	−0.623075	−0.311538	+	0.950234i	$0.600844\pi$
$264$	0.0229675	0.00141355
$265$	9.11908	0.560180
$266$	0	0
$267$	−0.0167708	−0.00102636
$268$	−8.96291	−0.547497
$269$	−12.9812	−0.791477	−0.395738	−	0.918363i	$-0.629511\pi$
$269$	−12.9812	−0.791477	−0.395738	+	0.918363i	$0.629511\pi$
$270$	−0.0298599	−0.00181721
$271$	26.7608	1.62560	0.812802	−	0.582540i	$-0.197941\pi$
$271$	26.7608	1.62560	0.812802	+	0.582540i	$0.197941\pi$
$272$	−6.75875	−0.409809
$273$	0.0171623	0.00103871
$274$	7.33889	0.443358
$275$	18.8087	1.13421
$276$	0.00432971	0.000260618 0
$277$	−2.44668	−0.147007	−0.0735033	−	0.997295i	$-0.523418\pi$
$277$	−2.44668	−0.147007	−0.0735033	+	0.997295i	$0.523418\pi$
$278$	0.503371	0.0301902
$279$	6.07681	0.363809
$280$	−1.04022	−0.0621650
$281$	0.0434072	0.00258945	0.00129473	−	0.999999i	$-0.499588\pi$
$281$	0.0434072	0.00258945	0.00129473	+	0.999999i	$0.499588\pi$
$282$	−0.0405827	−0.00241666
$283$	−1.19240	−0.0708806	−0.0354403	−	0.999372i	$-0.511283\pi$
$283$	−1.19240	−0.0708806	−0.0354403	+	0.999372i	$0.511283\pi$
$284$	−8.59288	−0.509893
$285$	0	0
$286$	−17.2212	−1.01831
$287$	8.12230	0.479444
$288$	2.99998	0.176775
$289$	28.6807	1.68710
$290$	−3.27179	−0.192126
$291$	−0.0748291	−0.00438656
$292$	13.5766	0.794513
$293$	11.8143	0.690202	0.345101	−	0.938566i	$-0.387845\pi$
$293$	11.8143	0.690202	0.345101	+	0.938566i	$0.387845\pi$
$294$	−0.00478425	−0.000279023 0
$295$	−1.56557	−0.0911511
$296$	9.28058	0.539423
$297$	0.137804	0.00799623
$298$	3.06660	0.177643
$299$	−3.24645	−0.187747
$300$	−0.0187444	−0.00108221
$301$	−10.7453	−0.619352
$302$	−8.09348	−0.465728
$303$	−0.0777684	−0.00446768
$304$	0	0
$305$	10.9844	0.628967
$306$	−20.2761	−1.15911
$307$	−24.5780	−1.40274	−0.701369	−	0.712798i	$-0.747427\pi$
$307$	−24.5780	−1.40274	−0.701369	+	0.712798i	$0.747427\pi$
$308$	4.80065	0.273543
$309$	0.0533395	0.00303438
$310$	−2.10709	−0.119675
$311$	−1.87051	−0.106067	−0.0530336	−	0.998593i	$-0.516889\pi$
$311$	−1.87051	−0.106067	−0.0530336	+	0.998593i	$0.516889\pi$
$312$	0.0171623	0.000971627 0
$313$	16.2468	0.918324	0.459162	−	0.888353i	$-0.348150\pi$
$313$	16.2468	0.918324	0.459162	+	0.888353i	$0.348150\pi$
$314$	−10.6799	−0.602702
$315$	−3.12063	−0.175828
$316$	14.4598	0.813426
$317$	5.96617	0.335094	0.167547	−	0.985864i	$-0.446415\pi$
$317$	5.96617	0.335094	0.167547	+	0.985864i	$0.446415\pi$
$318$	0.0419411	0.00235194
$319$	15.0994	0.845406
$320$	−1.04022	−0.0581500
$321$	0.0212286	0.00118487
$322$	0.904993	0.0504333
$323$	0	0
$324$	8.99979	0.499989
$325$	14.0547	0.779614
$326$	16.2677	0.900986
$327$	0.0488329	0.00270047
$328$	8.12230	0.448479
$329$	−8.48256	−0.467659
$330$	−0.0238912	−0.00131517
$331$	18.5340	1.01872	0.509359	−	0.860554i	$-0.329882\pi$
$331$	18.5340	1.01872	0.509359	+	0.860554i	$0.329882\pi$
$332$	0.247904	0.0136055
$333$	27.8415	1.52571
$334$	15.2244	0.833042
$335$	9.32339	0.509391
$336$	−0.00478425	−0.000261002 0
$337$	0.172579	0.00940096	0.00470048	−	0.999989i	$-0.498504\pi$
$337$	0.172579	0.00940096	0.00470048	+	0.999989i	$0.498504\pi$
$338$	0.131544	0.00715504
$339$	0.0805167	0.00437307
$340$	7.03058	0.381287
$341$	9.72429	0.526600
$342$	0	0
$343$	−1.00000	−0.0539949
$344$	−10.7453	−0.579350
$345$	−0.00450385	−0.000242479 0
$346$	0.0992419	0.00533528
$347$	14.2762	0.766388	0.383194	−	0.923668i	$-0.374824\pi$
$347$	14.2762	0.766388	0.383194	+	0.923668i	$0.374824\pi$
$348$	−0.0150478	−0.000806648 0
$349$	22.8000	1.22046	0.610228	−	0.792226i	$-0.291078\pi$
$349$	22.8000	1.22046	0.610228	+	0.792226i	$0.291078\pi$
$350$	−3.91794	−0.209423
$351$	0.102974	0.00549633
$352$	4.80065	0.255876
$353$	−35.5611	−1.89273	−0.946364	−	0.323103i	$-0.895274\pi$
$353$	−35.5611	−1.89273	−0.946364	+	0.323103i	$0.895274\pi$
$354$	−0.00720048	−0.000382701 0
$355$	8.93848	0.474405
$356$	−3.50543	−0.185787
$357$	0.0323355	0.00171138
$358$	3.77228	0.199371
$359$	−0.370131	−0.0195348	−0.00976738	−	0.999952i	$-0.503109\pi$
$359$	−0.370131	−0.0195348	−0.00976738	+	0.999952i	$0.503109\pi$
$360$	−3.12063	−0.164472
$361$	0	0
$362$	−11.1776	−0.587483
$363$	0.0576323	0.00302491
$364$	3.58726	0.188024
$365$	−14.1227	−0.739216
$366$	0.0505203	0.00264074
$367$	10.7741	0.562405	0.281202	−	0.959648i	$-0.409267\pi$
$367$	10.7741	0.562405	0.281202	+	0.959648i	$0.409267\pi$
$368$	0.904993	0.0471760
$369$	24.3667	1.26848
$370$	−9.65385	−0.501880
$371$	8.76649	0.455134
$372$	−0.00969106	−0.000502458 0
$373$	−7.48553	−0.387586	−0.193793	−	0.981042i	$-0.562079\pi$
$373$	−7.48553	−0.387586	−0.193793	+	0.981042i	$0.562079\pi$
$374$	−32.4464	−1.67776
$375$	0.0443816	0.00229186
$376$	−8.48256	−0.437455
$377$	11.2830	0.581103
$378$	−0.0287054	−0.00147644
$379$	−9.18749	−0.471930	−0.235965	−	0.971762i	$-0.575825\pi$
$379$	−9.18749	−0.471930	−0.235965	+	0.971762i	$0.575825\pi$
$380$	0	0
$381$	−0.0770222	−0.00394597
$382$	−6.03722	−0.308891
$383$	4.84048	0.247337	0.123668	−	0.992324i	$-0.460534\pi$
$383$	4.84048	0.247337	0.123668	+	0.992324i	$0.460534\pi$
$384$	−0.00478425	−0.000244145 0
$385$	−4.99373	−0.254504
$386$	19.2872	0.981694
$387$	−32.2358	−1.63864
$388$	−15.6407	−0.794038
$389$	−27.7529	−1.40713	−0.703565	−	0.710631i	$-0.748410\pi$
$389$	−27.7529	−1.40713	−0.703565	+	0.710631i	$0.748410\pi$
$390$	−0.0178526	−0.000904002 0
$391$	−6.11662	−0.309331
$392$	−1.00000	−0.0505076
$393$	0.000542955 0	2.73885e−5 0
$394$	7.25265	0.365383
$395$	−15.0413	−0.756812
$396$	14.4018	0.723720
$397$	12.0076	0.602643	0.301321	−	0.953523i	$-0.402572\pi$
$397$	12.0076	0.602643	0.301321	+	0.953523i	$0.402572\pi$
$398$	−11.0987	−0.556327
$399$	0	0
$400$	−3.91794	−0.195897
$401$	15.3814	0.768110	0.384055	−	0.923310i	$-0.374527\pi$
$401$	15.3814	0.768110	0.384055	+	0.923310i	$0.374527\pi$
$402$	0.0428808	0.00213870
$403$	7.26643	0.361967
$404$	−16.2551	−0.808721
$405$	−9.36176	−0.465190
$406$	−3.14529	−0.156098
$407$	44.5529	2.20840
$408$	0.0323355	0.00160085
$409$	−8.29530	−0.410176	−0.205088	−	0.978744i	$-0.565748\pi$
$409$	−8.29530	−0.410176	−0.205088	+	0.978744i	$0.565748\pi$
$410$	−8.44897	−0.417265
$411$	−0.0351110	−0.00173190
$412$	11.1490	0.549271
$413$	−1.50504	−0.0740582
$414$	2.71496	0.133433
$415$	−0.257875	−0.0126586
$416$	3.58726	0.175880
$417$	−0.00240825	−0.000117933 0
$418$	0	0
$419$	−23.0993	−1.12847	−0.564237	−	0.825613i	$-0.690830\pi$
$419$	−23.0993	−1.12847	−0.564237	+	0.825613i	$0.690830\pi$
$420$	0.00497667	0.000242836 0
$421$	13.7077	0.668070	0.334035	−	0.942561i	$-0.391590\pi$
$421$	13.7077	0.668070	0.334035	+	0.942561i	$0.391590\pi$
$422$	11.5491	0.562199
$423$	−25.4475	−1.23730
$424$	8.76649	0.425738
$425$	26.4804	1.28449
$426$	0.0411104	0.00199181
$427$	10.5597	0.511021
$428$	4.43719	0.214480
$429$	0.0823905	0.00397785
$430$	11.1775	0.539028
$431$	−37.6058	−1.81141	−0.905703	−	0.423913i	$-0.860656\pi$
$431$	−37.6058	−1.81141	−0.905703	+	0.423913i	$0.860656\pi$
$432$	−0.0287054	−0.00138109
$433$	−35.4280	−1.70256	−0.851281	−	0.524710i	$-0.824174\pi$
$433$	−35.4280	−1.70256	−0.851281	+	0.524710i	$0.824174\pi$
$434$	−2.02562	−0.0972329
$435$	0.0156530	0.000750506 0
$436$	10.2070	0.488828
$437$	0	0
$438$	−0.0649540	−0.00310362
$439$	−7.60746	−0.363084	−0.181542	−	0.983383i	$-0.558109\pi$
$439$	−7.60746	−0.363084	−0.181542	+	0.983383i	$0.558109\pi$
$440$	−4.99373	−0.238067
$441$	−2.99998	−0.142856
$442$	−24.2454	−1.15324
$443$	−13.1929	−0.626812	−0.313406	−	0.949619i	$-0.601470\pi$
$443$	−13.1929	−0.626812	−0.313406	+	0.949619i	$0.601470\pi$
$444$	−0.0444006	−0.00210716
$445$	3.64641	0.172857
$446$	11.9313	0.564965
$447$	−0.0146714	−0.000693932 0
$448$	−1.00000	−0.0472456
$449$	−3.58885	−0.169368	−0.0846842	−	0.996408i	$-0.526988\pi$
$449$	−3.58885	−0.169368	−0.0846842	+	0.996408i	$0.526988\pi$
$450$	−11.7537	−0.554077
$451$	38.9923	1.83608
$452$	16.8296	0.791596
$453$	0.0387212	0.00181928
$454$	14.7425	0.691901
$455$	−3.73154	−0.174937
$456$	0	0
$457$	−11.8277	−0.553278	−0.276639	−	0.960974i	$-0.589221\pi$
$457$	−11.8277	−0.553278	−0.276639	+	0.960974i	$0.589221\pi$
$458$	5.04641	0.235803
$459$	0.194012	0.00905572
$460$	−0.941391	−0.0438926
$461$	28.7095	1.33713	0.668567	−	0.743652i	$-0.266908\pi$
$461$	28.7095	1.33713	0.668567	+	0.743652i	$0.266908\pi$
$462$	−0.0229675	−0.00106854
$463$	6.56369	0.305041	0.152520	−	0.988300i	$-0.451261\pi$
$463$	6.56369	0.305041	0.152520	+	0.988300i	$0.451261\pi$
$464$	−3.14529	−0.146016
$465$	0.0100808	0.000467487 0
$466$	−5.11488	−0.236942
$467$	42.3126	1.95799	0.978997	−	0.203876i	$-0.0653539\pi$
$467$	42.3126	1.95799	0.978997	+	0.203876i	$0.0653539\pi$
$468$	10.7617	0.497460
$469$	8.96291	0.413869
$470$	8.82373	0.407008
$471$	0.0510953	0.00235435
$472$	−1.50504	−0.0692751
$473$	−51.5847	−2.37187
$474$	−0.0691791	−0.00317750
$475$	0	0
$476$	6.75875	0.309787
$477$	26.2993	1.20416
$478$	21.8093	0.997533
$479$	24.2750	1.10915	0.554576	−	0.832133i	$-0.312880\pi$
$479$	24.2750	1.10915	0.554576	+	0.832133i	$0.312880\pi$
$480$	0.00497667	0.000227153 0
$481$	33.2919	1.51798
$482$	1.76058	0.0801922
$483$	−0.00432971	−0.000197009 0
$484$	12.0463	0.547557
$485$	16.2698	0.738774
$486$	−0.129173	−0.00585942
$487$	−18.5708	−0.841522	−0.420761	−	0.907172i	$-0.638237\pi$
$487$	−18.5708	−0.841522	−0.420761	+	0.907172i	$0.638237\pi$
$488$	10.5597	0.478016
$489$	−0.0778288	−0.00351954
$490$	1.04022	0.0469923
$491$	9.36188	0.422496	0.211248	−	0.977433i	$-0.432247\pi$
$491$	9.36188	0.422496	0.211248	+	0.977433i	$0.432247\pi$
$492$	−0.0388591	−0.00175190
$493$	21.2582	0.957421
$494$	0	0
$495$	−14.9811	−0.673350
$496$	−2.02562	−0.0909530
$497$	8.59288	0.385443
$498$	−0.00118604	−5.31475e−5 0
$499$	40.6920	1.82162	0.910812	−	0.412821i	$-0.135457\pi$
$499$	40.6920	1.82162	0.910812	+	0.412821i	$0.135457\pi$
$500$	9.27662	0.414863
$501$	−0.0728373	−0.00325413
$502$	16.8967	0.754138
$503$	3.70005	0.164977	0.0824885	−	0.996592i	$-0.473713\pi$
$503$	3.70005	0.164977	0.0824885	+	0.996592i	$0.473713\pi$
$504$	−2.99998	−0.133630
$505$	16.9089	0.752434
$506$	4.34456	0.193139
$507$	−0.000629338 0	−2.79499e−5 0
$508$	−16.0991	−0.714284
$509$	−10.7839	−0.477989	−0.238994	−	0.971021i	$-0.576818\pi$
$509$	−10.7839	−0.477989	−0.238994	+	0.971021i	$0.576818\pi$
$510$	−0.0336360	−0.00148943
$511$	−13.5766	−0.600596
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	8.77380	0.386996
$515$	−11.5974	−0.511042
$516$	0.0514084	0.00226313
$517$	−40.7218	−1.79094
$518$	−9.28058	−0.407765
$519$	−0.000474798 0	−2.08413e−5 0
$520$	−3.73154	−0.163639
$521$	−30.7942	−1.34912	−0.674560	−	0.738220i	$-0.735666\pi$
$521$	−30.7942	−1.34912	−0.674560	+	0.738220i	$0.735666\pi$
$522$	−9.43579	−0.412993
$523$	−19.8448	−0.867752	−0.433876	−	0.900973i	$-0.642854\pi$
$523$	−19.8448	−0.867752	−0.433876	+	0.900973i	$0.642854\pi$
$524$	0.113488	0.00495775
$525$	0.0187444	0.000818073 0
$526$	10.1046	0.440581
$527$	13.6907	0.596374
$528$	−0.0229675	−0.000999532 0
$529$	−22.1810	−0.964391
$530$	−9.11908	−0.396107
$531$	−4.51508	−0.195938
$532$	0	0
$533$	29.1368	1.26206
$534$	0.0167708	0.000725745 0
$535$	−4.61565	−0.199552
$536$	8.96291	0.387139
$537$	−0.0180475	−0.000778807 0
$538$	12.9812	0.559659
$539$	−4.80065	−0.206779
$540$	0.0298599	0.00128496
$541$	−22.6165	−0.972357	−0.486179	−	0.873859i	$-0.661610\pi$
$541$	−22.6165	−0.972357	−0.486179	+	0.873859i	$0.661610\pi$
$542$	−26.7608	−1.14948
$543$	0.0534765	0.00229490
$544$	6.75875	0.289779
$545$	−10.6175	−0.454806
$546$	−0.0171623	−0.000734481 0
$547$	−22.3199	−0.954328	−0.477164	−	0.878814i	$-0.658335\pi$
$547$	−22.3199	−0.954328	−0.477164	+	0.878814i	$0.658335\pi$
$548$	−7.33889	−0.313502
$549$	31.6789	1.35202
$550$	−18.8087	−0.802005
$551$	0	0
$552$	−0.00432971	−0.000184285 0
$553$	−14.4598	−0.614892
$554$	2.44668	0.103949
$555$	0.0461864	0.00196050
$556$	−0.503371	−0.0213477
$557$	23.4256	0.992576	0.496288	−	0.868158i	$-0.334696\pi$
$557$	23.4256	0.992576	0.496288	+	0.868158i	$0.334696\pi$
$558$	−6.07681	−0.257252
$559$	−38.5464	−1.63034
$560$	1.04022	0.0439573
$561$	0.155232	0.00655388
$562$	−0.0434072	−0.00183102
$563$	34.0131	1.43348	0.716741	−	0.697339i	$-0.245633\pi$
$563$	34.0131	1.43348	0.716741	+	0.697339i	$0.245633\pi$
$564$	0.0405827	0.00170884
$565$	−17.5064	−0.736501
$566$	1.19240	0.0501202
$567$	−8.99979	−0.377956
$568$	8.59288	0.360549
$569$	−4.30472	−0.180463	−0.0902317	−	0.995921i	$-0.528761\pi$
$569$	−4.30472	−0.180463	−0.0902317	+	0.995921i	$0.528761\pi$
$570$	0	0
$571$	12.1839	0.509879	0.254939	−	0.966957i	$-0.417944\pi$
$571$	12.1839	0.509879	0.254939	+	0.966957i	$0.417944\pi$
$572$	17.2212	0.720055
$573$	0.0288835	0.00120663
$574$	−8.12230	−0.339018
$575$	−3.54571	−0.147866
$576$	−2.99998	−0.124999
$577$	4.50701	0.187629	0.0938147	−	0.995590i	$-0.470094\pi$
$577$	4.50701	0.187629	0.0938147	+	0.995590i	$0.470094\pi$
$578$	−28.6807	−1.19296
$579$	−0.0922749	−0.00383481
$580$	3.27179	0.135854
$581$	−0.247904	−0.0102848
$582$	0.0748291	0.00310177
$583$	42.0849	1.74298
$584$	−13.5766	−0.561806
$585$	−11.1945	−0.462837
$586$	−11.8143	−0.488046
$587$	−27.6353	−1.14063	−0.570316	−	0.821426i	$-0.693179\pi$
$587$	−27.6353	−1.14063	−0.570316	+	0.821426i	$0.693179\pi$
$588$	0.00478425	0.000197299 0
$589$	0	0
$590$	1.56557	0.0644536
$591$	−0.0346985	−0.00142730
$592$	−9.28058	−0.381430
$593$	17.2410	0.708005	0.354002	−	0.935245i	$-0.384820\pi$
$593$	17.2410	0.708005	0.354002	+	0.935245i	$0.384820\pi$
$594$	−0.137804	−0.00565419
$595$	−7.03058	−0.288226
$596$	−3.06660	−0.125613
$597$	0.0530989	0.00217319
$598$	3.24645	0.132757
$599$	29.9923	1.22545	0.612726	−	0.790296i	$-0.290073\pi$
$599$	29.9923	1.22545	0.612726	+	0.790296i	$0.290073\pi$
$600$	0.0187444	0.000765237 0
$601$	−18.9890	−0.774576	−0.387288	−	0.921959i	$-0.626588\pi$
$601$	−18.9890	−0.774576	−0.387288	+	0.921959i	$0.626588\pi$
$602$	10.7453	0.437948
$603$	26.8885	1.09499
$604$	8.09348	0.329319
$605$	−12.5308	−0.509447
$606$	0.0777684	0.00315912
$607$	31.6295	1.28380	0.641901	−	0.766787i	$-0.278146\pi$
$607$	31.6295	1.28380	0.641901	+	0.766787i	$0.278146\pi$
$608$	0	0
$609$	0.0150478	0.000609769 0
$610$	−10.9844	−0.444747
$611$	−30.4292	−1.23103
$612$	20.2761	0.819612
$613$	3.46337	0.139884	0.0699421	−	0.997551i	$-0.477719\pi$
$613$	3.46337	0.139884	0.0699421	+	0.997551i	$0.477719\pi$
$614$	24.5780	0.991885
$615$	0.0404220	0.00162997
$616$	−4.80065	−0.193424
$617$	23.0192	0.926719	0.463360	−	0.886170i	$-0.346644\pi$
$617$	23.0192	0.926719	0.463360	+	0.886170i	$0.346644\pi$
$618$	−0.0533395	−0.00214563
$619$	33.0177	1.32709	0.663547	−	0.748134i	$-0.269050\pi$
$619$	33.0177	1.32709	0.663547	+	0.748134i	$0.269050\pi$
$620$	2.10709	0.0846227
$621$	−0.0259782	−0.00104247
$622$	1.87051	0.0750008
$623$	3.50543	0.140442
$624$	−0.0171623	−0.000687044 0
$625$	9.94000	0.397600
$626$	−16.2468	−0.649353
$627$	0	0
$628$	10.6799	0.426175
$629$	62.7251	2.50101
$630$	3.12063	0.124329
$631$	−14.2779	−0.568393	−0.284196	−	0.958766i	$-0.591727\pi$
$631$	−14.2779	−0.568393	−0.284196	+	0.958766i	$0.591727\pi$
$632$	−14.4598	−0.575179
$633$	−0.0552535	−0.00219613
$634$	−5.96617	−0.236947
$635$	16.7466	0.664570
$636$	−0.0419411	−0.00166307
$637$	−3.58726	−0.142133
$638$	−15.0994	−0.597792
$639$	25.7784	1.01978
$640$	1.04022	0.0411183
$641$	14.3005	0.564836	0.282418	−	0.959291i	$-0.408863\pi$
$641$	14.3005	0.564836	0.282418	+	0.959291i	$0.408863\pi$
$642$	−0.0212286	−0.000837826 0
$643$	−5.12366	−0.202058	−0.101029	−	0.994884i	$-0.532213\pi$
$643$	−5.12366	−0.202058	−0.101029	+	0.994884i	$0.532213\pi$
$644$	−0.904993	−0.0356617
$645$	−0.0534760	−0.00210562
$646$	0	0
$647$	−1.44261	−0.0567148	−0.0283574	−	0.999598i	$-0.509028\pi$
$647$	−1.44261	−0.0567148	−0.0283574	+	0.999598i	$0.509028\pi$
$648$	−8.99979	−0.353545
$649$	−7.22517	−0.283613
$650$	−14.0547	−0.551270
$651$	0.00969106	0.000379823 0
$652$	−16.2677	−0.637093
$653$	−31.3378	−1.22634	−0.613171	−	0.789950i	$-0.710107\pi$
$653$	−31.3378	−1.22634	−0.613171	+	0.789950i	$0.710107\pi$
$654$	−0.0488329	−0.00190952
$655$	−0.118053	−0.00461269
$656$	−8.12230	−0.317122
$657$	−40.7296	−1.58901
$658$	8.48256	0.330685
$659$	14.3545	0.559173	0.279587	−	0.960120i	$-0.409803\pi$
$659$	14.3545	0.559173	0.279587	+	0.960120i	$0.409803\pi$
$660$	0.0238912	0.000929965 0
$661$	37.5574	1.46081	0.730407	−	0.683013i	$-0.239331\pi$
$661$	37.5574	1.46081	0.730407	+	0.683013i	$0.239331\pi$
$662$	−18.5340	−0.720343
$663$	0.115996	0.00450491
$664$	−0.247904	−0.00962056
$665$	0	0
$666$	−27.8415	−1.07884
$667$	−2.84646	−0.110215
$668$	−15.2244	−0.589050
$669$	−0.0570824	−0.00220693
$670$	−9.32339	−0.360194
$671$	50.6936	1.95700
$672$	0.00478425	0.000184556 0
$673$	33.8136	1.30342	0.651709	−	0.758469i	$-0.274052\pi$
$673$	33.8136	1.30342	0.651709	+	0.758469i	$0.274052\pi$
$674$	−0.172579	−0.00664749
$675$	0.112466	0.00432882
$676$	−0.131544	−0.00505938
$677$	−39.7472	−1.52761	−0.763805	−	0.645447i	$-0.776671\pi$
$677$	−39.7472	−1.52761	−0.763805	+	0.645447i	$0.776671\pi$
$678$	−0.0805167	−0.00309223
$679$	15.6407	0.600236
$680$	−7.03058	−0.269610
$681$	−0.0705319	−0.00270279
$682$	−9.72429	−0.372362
$683$	−47.9170	−1.83349	−0.916746	−	0.399470i	$-0.869194\pi$
$683$	−47.9170	−1.83349	−0.916746	+	0.399470i	$0.869194\pi$
$684$	0	0
$685$	7.63405	0.291682
$686$	1.00000	0.0381802
$687$	−0.0241433	−0.000921123 0
$688$	10.7453	0.409663
$689$	31.4477	1.19806
$690$	0.00450385	0.000171459 0
$691$	9.25021	0.351895	0.175947	−	0.984400i	$-0.443701\pi$
$691$	9.25021	0.351895	0.175947	+	0.984400i	$0.443701\pi$
$692$	−0.0992419	−0.00377261
$693$	−14.4018	−0.547081
$694$	−14.2762	−0.541918
$695$	0.523617	0.0198619
$696$	0.0150478	0.000570387 0
$697$	54.8966	2.07936
$698$	−22.8000	−0.862992
$699$	0.0244708	0.000925572 0
$700$	3.91794	0.148084
$701$	−36.7507	−1.38806	−0.694028	−	0.719948i	$-0.744166\pi$
$701$	−36.7507	−1.38806	−0.694028	+	0.719948i	$0.744166\pi$
$702$	−0.102974	−0.00388649
$703$	0	0
$704$	−4.80065	−0.180931
$705$	−0.0422149	−0.00158990
$706$	35.5611	1.33836
$707$	16.2551	0.611336
$708$	0.00720048	0.000270611 0
$709$	9.65553	0.362621	0.181311	−	0.983426i	$-0.441966\pi$
$709$	9.65553	0.362621	0.181311	+	0.983426i	$0.441966\pi$
$710$	−8.93848	−0.335455
$711$	−43.3790	−1.62684
$712$	3.50543	0.131371
$713$	−1.83317	−0.0686528
$714$	−0.0323355	−0.00121013
$715$	−17.9138	−0.669939
$716$	−3.77228	−0.140977
$717$	−0.104341	−0.00389668
$718$	0.370131	0.0138132
$719$	37.1060	1.38382	0.691910	−	0.721983i	$-0.256769\pi$
$719$	37.1060	1.38382	0.691910	+	0.721983i	$0.256769\pi$
$720$	3.12063	0.116299
$721$	−11.1490	−0.415210
$722$	0	0
$723$	−0.00842305	−0.000313256 0
$724$	11.1776	0.415413
$725$	12.3231	0.457667
$726$	−0.0576323	−0.00213893
$727$	1.86645	0.0692229	0.0346115	−	0.999401i	$-0.488981\pi$
$727$	1.86645	0.0692229	0.0346115	+	0.999401i	$0.488981\pi$
$728$	−3.58726	−0.132953
$729$	−26.9988	−0.999954
$730$	14.1227	0.522704
$731$	−72.6251	−2.68614
$732$	−0.0505203	−0.00186729
$733$	−7.19348	−0.265697	−0.132849	−	0.991136i	$-0.542412\pi$
$733$	−7.19348	−0.265697	−0.132849	+	0.991136i	$0.542412\pi$
$734$	−10.7741	−0.397680
$735$	−0.00497667	−0.000183567 0
$736$	−0.904993	−0.0333585
$737$	43.0278	1.58495
$738$	−24.3667	−0.896951
$739$	19.1091	0.702941	0.351470	−	0.936199i	$-0.385682\pi$
$739$	19.1091	0.702941	0.351470	+	0.936199i	$0.385682\pi$
$740$	9.65385	0.354882
$741$	0	0
$742$	−8.76649	−0.321828
$743$	−29.8383	−1.09466	−0.547330	−	0.836917i	$-0.684356\pi$
$743$	−29.8383	−1.09466	−0.547330	+	0.836917i	$0.684356\pi$
$744$	0.00969106	0.000355292 0
$745$	3.18994	0.116870
$746$	7.48553	0.274065
$747$	−0.743708	−0.0272108
$748$	32.4464	1.18636
$749$	−4.43719	−0.162131
$750$	−0.0443816	−0.00162059
$751$	9.26453	0.338068	0.169034	−	0.985610i	$-0.445935\pi$
$751$	9.26453	0.338068	0.169034	+	0.985610i	$0.445935\pi$
$752$	8.48256	0.309327
$753$	−0.0808381	−0.00294590
$754$	−11.2830	−0.410902
$755$	−8.41900	−0.306399
$756$	0.0287054	0.00104400
$757$	−5.22390	−0.189866	−0.0949330	−	0.995484i	$-0.530264\pi$
$757$	−5.22390	−0.189866	−0.0949330	+	0.995484i	$0.530264\pi$
$758$	9.18749	0.333705
$759$	−0.0207854	−0.000754463 0
$760$	0	0
$761$	−0.690447	−0.0250287	−0.0125143	−	0.999922i	$-0.503984\pi$
$761$	−0.690447	−0.0250287	−0.0125143	+	0.999922i	$0.503984\pi$
$762$	0.0770222	0.00279022
$763$	−10.2070	−0.369519
$764$	6.03722	0.218419
$765$	−21.0916	−0.762568
$766$	−4.84048	−0.174894
$767$	−5.39897	−0.194946
$768$	0.00478425	0.000172637 0
$769$	−21.7334	−0.783726	−0.391863	−	0.920024i	$-0.628169\pi$
$769$	−21.7334	−0.783726	−0.391863	+	0.920024i	$0.628169\pi$
$770$	4.99373	0.179962
$771$	−0.0419760	−0.00151173
$772$	−19.2872	−0.694163
$773$	−3.07950	−0.110762	−0.0553809	−	0.998465i	$-0.517637\pi$
$773$	−3.07950	−0.110762	−0.0553809	+	0.998465i	$0.517637\pi$
$774$	32.2358	1.15869
$775$	7.93626	0.285079
$776$	15.6407	0.561470
$777$	0.0444006	0.00159286
$778$	27.7529	0.994991
$779$	0	0
$780$	0.0178526	0.000639226 0
$781$	41.2514	1.47609
$782$	6.11662	0.218730
$783$	0.0902866	0.00322658
$784$	1.00000	0.0357143
$785$	−11.1094	−0.396513
$786$	−0.000542955 0	−1.93666e−5 0
$787$	−16.8695	−0.601334	−0.300667	−	0.953729i	$-0.597209\pi$
$787$	−16.8695	−0.601334	−0.300667	+	0.953729i	$0.597209\pi$
$788$	−7.25265	−0.258365
$789$	−0.0483428	−0.00172105
$790$	15.0413	0.535147
$791$	−16.8296	−0.598390
$792$	−14.4018	−0.511747
$793$	37.8805	1.34518
$794$	−12.0076	−0.426133
$795$	0.0436279	0.00154732
$796$	11.0987	0.393383
$797$	−7.30912	−0.258902	−0.129451	−	0.991586i	$-0.541322\pi$
$797$	−7.30912	−0.258902	−0.129451	+	0.991586i	$0.541322\pi$
$798$	0	0
$799$	−57.3315	−2.02824
$800$	3.91794	0.138520
$801$	10.5162	0.371572
$802$	−15.3814	−0.543135
$803$	−65.1768	−2.30004
$804$	−0.0428808	−0.00151229
$805$	0.941391	0.0331797
$806$	−7.26643	−0.255949
$807$	−0.0621052	−0.00218621
$808$	16.2551	0.571852
$809$	−14.4990	−0.509757	−0.254878	−	0.966973i	$-0.582035\pi$
$809$	−14.4990	−0.509757	−0.254878	+	0.966973i	$0.582035\pi$
$810$	9.36176	0.328939
$811$	−7.40688	−0.260091	−0.130045	−	0.991508i	$-0.541512\pi$
$811$	−7.40688	−0.260091	−0.130045	+	0.991508i	$0.541512\pi$
$812$	3.14529	0.110378
$813$	0.128030	0.00449022
$814$	−44.5529	−1.56158
$815$	16.9220	0.592752
$816$	−0.0323355	−0.00113197
$817$	0	0
$818$	8.29530	0.290038
$819$	−10.7617	−0.376044
$820$	8.44897	0.295051
$821$	41.5767	1.45104	0.725518	−	0.688203i	$-0.241600\pi$
$821$	41.5767	1.45104	0.725518	+	0.688203i	$0.241600\pi$
$822$	0.0351110	0.00122464
$823$	−30.7292	−1.07115	−0.535577	−	0.844486i	$-0.679906\pi$
$823$	−30.7292	−1.07115	−0.535577	+	0.844486i	$0.679906\pi$
$824$	−11.1490	−0.388393
$825$	0.0899854	0.00313289
$826$	1.50504	0.0523670
$827$	39.6817	1.37987	0.689933	−	0.723873i	$-0.257640\pi$
$827$	39.6817	1.37987	0.689933	+	0.723873i	$0.257640\pi$
$828$	−2.71496	−0.0943513
$829$	18.5029	0.642631	0.321316	−	0.946972i	$-0.395875\pi$
$829$	18.5029	0.642631	0.321316	+	0.946972i	$0.395875\pi$
$830$	0.257875	0.00895097
$831$	−0.0117055	−0.000406060 0
$832$	−3.58726	−0.124366
$833$	−6.75875	−0.234177
$834$	0.00240825	8.33910e−5 0
$835$	15.8367	0.548052
$836$	0	0
$837$	0.0581462	0.00200983
$838$	23.0993	0.797952
$839$	11.4011	0.393610	0.196805	−	0.980443i	$-0.436943\pi$
$839$	11.4011	0.393610	0.196805	+	0.980443i	$0.436943\pi$
$840$	−0.00497667	−0.000171711 0
$841$	−19.1072	−0.658868
$842$	−13.7077	−0.472397
$843$	0.000207671 0	7.15255e−6 0
$844$	−11.5491	−0.397535
$845$	0.136835	0.00470725
$846$	25.4475	0.874903
$847$	−12.0463	−0.413914
$848$	−8.76649	−0.301043
$849$	−0.00570472	−0.000195785 0
$850$	−26.4804	−0.908270
$851$	−8.39886	−0.287909
$852$	−0.0411104	−0.00140842
$853$	48.8923	1.67404	0.837020	−	0.547173i	$-0.184296\pi$
$853$	48.8923	1.67404	0.837020	+	0.547173i	$0.184296\pi$
$854$	−10.5597	−0.361346
$855$	0	0
$856$	−4.43719	−0.151660
$857$	−9.15789	−0.312828	−0.156414	−	0.987692i	$-0.549993\pi$
$857$	−9.15789	−0.312828	−0.156414	+	0.987692i	$0.549993\pi$
$858$	−0.0823905	−0.00281276
$859$	−42.5285	−1.45105	−0.725526	−	0.688195i	$-0.758404\pi$
$859$	−42.5285	−1.45105	−0.725526	+	0.688195i	$0.758404\pi$
$860$	−11.1775	−0.381150
$861$	0.0388591	0.00132431
$862$	37.6058	1.28086
$863$	−47.4755	−1.61609	−0.808043	−	0.589124i	$-0.799473\pi$
$863$	−47.4755	−1.61609	−0.808043	+	0.589124i	$0.799473\pi$
$864$	0.0287054	0.000976576 0
$865$	0.103233	0.00351004
$866$	35.4280	1.20389
$867$	0.137215	0.00466008
$868$	2.02562	0.0687540
$869$	−69.4164	−2.35479
$870$	−0.0156530	−0.000530688 0
$871$	32.1523	1.08944
$872$	−10.2070	−0.345653
$873$	46.9218	1.58806
$874$	0	0
$875$	−9.27662	−0.313607
$876$	0.0649540	0.00219459
$877$	−30.6985	−1.03662	−0.518308	−	0.855194i	$-0.673438\pi$
$877$	−30.6985	−1.03662	−0.518308	+	0.855194i	$0.673438\pi$
$878$	7.60746	0.256740
$879$	0.0565227	0.00190646
$880$	4.99373	0.168339
$881$	−1.58325	−0.0533411	−0.0266705	−	0.999644i	$-0.508491\pi$
$881$	−1.58325	−0.0533411	−0.0266705	+	0.999644i	$0.508491\pi$
$882$	2.99998	0.101014
$883$	16.0029	0.538541	0.269270	−	0.963065i	$-0.413217\pi$
$883$	16.0029	0.538541	0.269270	+	0.963065i	$0.413217\pi$
$884$	24.2454	0.815461
$885$	−0.00749008	−0.000251776 0
$886$	13.1929	0.443223
$887$	−39.2584	−1.31817	−0.659084	−	0.752070i	$-0.729056\pi$
$887$	−39.2584	−1.31817	−0.659084	+	0.752070i	$0.729056\pi$
$888$	0.0444006	0.00148999
$889$	16.0991	0.539948
$890$	−3.64641	−0.122228
$891$	−43.2049	−1.44742
$892$	−11.9313	−0.399491
$893$	0	0
$894$	0.0146714	0.000490684 0
$895$	3.92400	0.131165
$896$	1.00000	0.0334077
$897$	−0.0155318	−0.000518592 0
$898$	3.58885	0.119762
$899$	6.37116	0.212490
$900$	11.7537	0.391791
$901$	59.2505	1.97392
$902$	−38.9923	−1.29830
$903$	−0.0514084	−0.00171076
$904$	−16.8296	−0.559743
$905$	−11.6272	−0.386501
$906$	−0.0387212	−0.00128643
$907$	−34.6875	−1.15178	−0.575890	−	0.817527i	$-0.695344\pi$
$907$	−34.6875	−1.15178	−0.575890	+	0.817527i	$0.695344\pi$
$908$	−14.7425	−0.489248
$909$	48.7649	1.61743
$910$	3.73154	0.123699
$911$	56.0277	1.85628	0.928140	−	0.372232i	$-0.121408\pi$
$911$	56.0277	1.85628	0.928140	+	0.372232i	$0.121408\pi$
$912$	0	0
$913$	−1.19010	−0.0393867
$914$	11.8277	0.391226
$915$	0.0525522	0.00173732
$916$	−5.04641	−0.166738
$917$	−0.113488	−0.00374771
$918$	−0.194012	−0.00640336
$919$	−40.1786	−1.32537	−0.662685	−	0.748898i	$-0.730583\pi$
$919$	−40.1786	−1.32537	−0.662685	+	0.748898i	$0.730583\pi$
$920$	0.941391	0.0310368
$921$	−0.117587	−0.00387462
$922$	−28.7095	−0.945496
$923$	30.8249	1.01461
$924$	0.0229675	0.000755575 0
$925$	36.3608	1.19554
$926$	−6.56369	−0.215696
$927$	−33.4467	−1.09853
$928$	3.14529	0.103249
$929$	35.4329	1.16251	0.581257	−	0.813720i	$-0.302561\pi$
$929$	35.4329	1.16251	0.581257	+	0.813720i	$0.302561\pi$
$930$	−0.0100808	−0.000330564 0
$931$	0	0
$932$	5.11488	0.167543
$933$	−0.00894900	−0.000292977 0
$934$	−42.3126	−1.38451
$935$	−33.7514	−1.10379
$936$	−10.7617	−0.351757
$937$	34.3948	1.12363	0.561814	−	0.827263i	$-0.310103\pi$
$937$	34.3948	1.12363	0.561814	+	0.827263i	$0.310103\pi$
$938$	−8.96291	−0.292649
$939$	0.0777288	0.00253658
$940$	−8.82373	−0.287798
$941$	−3.28516	−0.107093	−0.0535466	−	0.998565i	$-0.517053\pi$
$941$	−3.28516	−0.107093	−0.0535466	+	0.998565i	$0.517053\pi$
$942$	−0.0510953	−0.00166477
$943$	−7.35062	−0.239369
$944$	1.50504	0.0489849
$945$	−0.0298599	−0.000971342 0
$946$	51.5847	1.67716
$947$	−0.832724	−0.0270599	−0.0135300	−	0.999908i	$-0.504307\pi$
$947$	−0.832724	−0.0270599	−0.0135300	+	0.999908i	$0.504307\pi$
$948$	0.0691791	0.00224683
$949$	−48.7030	−1.58097
$950$	0	0
$951$	0.0285436	0.000925591 0
$952$	−6.75875	−0.219052
$953$	−9.07457	−0.293954	−0.146977	−	0.989140i	$-0.546954\pi$
$953$	−9.07457	−0.293954	−0.146977	+	0.989140i	$0.546954\pi$
$954$	−26.2993	−0.851470
$955$	−6.28003	−0.203217
$956$	−21.8093	−0.705362
$957$	0.0722394	0.00233517
$958$	−24.2750	−0.784289
$959$	7.33889	0.236985
$960$	−0.00497667	−0.000160621 0
$961$	−26.8969	−0.867641
$962$	−33.2919	−1.07337
$963$	−13.3115	−0.428956
$964$	−1.76058	−0.0567044
$965$	20.0630	0.645849
$966$	0.00432971	0.000139306 0
$967$	−1.40731	−0.0452561	−0.0226281	−	0.999744i	$-0.507203\pi$
$967$	−1.40731	−0.0452561	−0.0226281	+	0.999744i	$0.507203\pi$
$968$	−12.0463	−0.387181
$969$	0	0
$970$	−16.2698	−0.522392
$971$	7.27429	0.233443	0.116722	−	0.993165i	$-0.462761\pi$
$971$	7.27429	0.233443	0.116722	+	0.993165i	$0.462761\pi$
$972$	0.129173	0.00414324
$973$	0.503371	0.0161373
$974$	18.5708	0.595046
$975$	0.0672411	0.00215344
$976$	−10.5597	−0.338009
$977$	−17.2745	−0.552660	−0.276330	−	0.961063i	$-0.589118\pi$
$977$	−17.2745	−0.552660	−0.276330	+	0.961063i	$0.589118\pi$
$978$	0.0778288	0.00248869
$979$	16.8283	0.537836
$980$	−1.04022	−0.0332286
$981$	−30.6208	−0.977648
$982$	−9.36188	−0.298750
$983$	−11.7662	−0.375282	−0.187641	−	0.982238i	$-0.560084\pi$
$983$	−11.7662	−0.375282	−0.187641	+	0.982238i	$0.560084\pi$
$984$	0.0388591	0.00123878
$985$	7.54435	0.240383
$986$	−21.2582	−0.676999
$987$	−0.0405827	−0.00129176
$988$	0	0
$989$	9.72446	0.309220
$990$	14.9811	0.476130
$991$	−7.94206	−0.252288	−0.126144	−	0.992012i	$-0.540260\pi$
$991$	−7.94206	−0.252288	−0.126144	+	0.992012i	$0.540260\pi$
$992$	2.02562	0.0643135
$993$	0.0886710	0.00281389
$994$	−8.59288	−0.272549
$995$	−11.5451	−0.366004
$996$	0.00118604	3.75810e−5 0
$997$	−21.6835	−0.686722	−0.343361	−	0.939203i	$-0.611565\pi$
$997$	−21.6835	−0.686722	−0.343361	+	0.939203i	$0.611565\pi$
$998$	−40.6920	−1.28808
$999$	0.266403	0.00842861

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5054.2.a.bj.1.5		9
19.3	odd	18		266.2.u.c.85.2	✓	18
19.13	odd	18		266.2.u.c.169.2	yes	18
19.18	odd	2		5054.2.a.bk.1.5		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
266.2.u.c.85.2	✓	18	19.3	odd	18
266.2.u.c.169.2	yes	18	19.13	odd	18
5054.2.a.bj.1.5		9	1.1	even	1	trivial
5054.2.a.bk.1.5		9	19.18	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 5054 = 2 \cdot 7 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5054.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.00478425 q^{3} +1.00000 q^{4} -1.04022 q^{5} -0.00478425 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.99998 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.00478425 q^{3} +1.00000 q^{4} -1.04022 q^{5} -0.00478425 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.99998 q^{9} +1.04022 q^{10} -4.80065 q^{11} +0.00478425 q^{12} -3.58726 q^{13} +1.00000 q^{14} -0.00497667 q^{15} +1.00000 q^{16} -6.75875 q^{17} +2.99998 q^{18} -1.04022 q^{20} -0.00478425 q^{21} +4.80065 q^{22} +0.904993 q^{23} -0.00478425 q^{24} -3.91794 q^{25} +3.58726 q^{26} -0.0287054 q^{27} -1.00000 q^{28} -3.14529 q^{29} +0.00497667 q^{30} -2.02562 q^{31} -1.00000 q^{32} -0.0229675 q^{33} +6.75875 q^{34} +1.04022 q^{35} -2.99998 q^{36} -9.28058 q^{37} -0.0171623 q^{39} +1.04022 q^{40} -8.12230 q^{41} +0.00478425 q^{42} +10.7453 q^{43} -4.80065 q^{44} +3.12063 q^{45} -0.904993 q^{46} +8.48256 q^{47} +0.00478425 q^{48} +1.00000 q^{49} +3.91794 q^{50} -0.0323355 q^{51} -3.58726 q^{52} -8.76649 q^{53} +0.0287054 q^{54} +4.99373 q^{55} +1.00000 q^{56} +3.14529 q^{58} +1.50504 q^{59} -0.00497667 q^{60} -10.5597 q^{61} +2.02562 q^{62} +2.99998 q^{63} +1.00000 q^{64} +3.73154 q^{65} +0.0229675 q^{66} -8.96291 q^{67} -6.75875 q^{68} +0.00432971 q^{69} -1.04022 q^{70} -8.59288 q^{71} +2.99998 q^{72} +13.5766 q^{73} +9.28058 q^{74} -0.0187444 q^{75} +4.80065 q^{77} +0.0171623 q^{78} +14.4598 q^{79} -1.04022 q^{80} +8.99979 q^{81} +8.12230 q^{82} +0.247904 q^{83} -0.00478425 q^{84} +7.03058 q^{85} -10.7453 q^{86} -0.0150478 q^{87} +4.80065 q^{88} -3.50543 q^{89} -3.12063 q^{90} +3.58726 q^{91} +0.904993 q^{92} -0.00969106 q^{93} -8.48256 q^{94} -0.00478425 q^{96} -15.6407 q^{97} -1.00000 q^{98} +14.4018 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 9 q^{2} - 3 q^{3} + 9 q^{4} + 3 q^{5} + 3 q^{6} - 9 q^{7} - 9 q^{8} + 12 q^{9}+O(q^{10}) \) 9 * q - 9 * q^2 - 3 * q^3 + 9 * q^4 + 3 * q^5 + 3 * q^6 - 9 * q^7 - 9 * q^8 + 12 * q^9	\( 9 q - 9 q^{2} - 3 q^{3} + 9 q^{4} + 3 q^{5} + 3 q^{6} - 9 q^{7} - 9 q^{8} + 12 q^{9} - 3 q^{10} - 3 q^{11} - 3 q^{12} - 12 q^{13} + 9 q^{14} + 6 q^{15} + 9 q^{16} + 12 q^{17} - 12 q^{18} + 3 q^{20} + 3 q^{21} + 3 q^{22} + 6 q^{23} + 3 q^{24} + 12 q^{26} - 24 q^{27} - 9 q^{28} + 6 q^{29} - 6 q^{30} - 9 q^{31} - 9 q^{32} + 3 q^{33} - 12 q^{34} - 3 q^{35} + 12 q^{36} - 9 q^{37} + 33 q^{39} - 3 q^{40} - 3 q^{41} - 3 q^{42} + 21 q^{43} - 3 q^{44} + 18 q^{45} - 6 q^{46} + 21 q^{47} - 3 q^{48} + 9 q^{49} - 39 q^{51} - 12 q^{52} + 24 q^{54} + 24 q^{55} + 9 q^{56} - 6 q^{58} + 9 q^{59} + 6 q^{60} + 6 q^{61} + 9 q^{62} - 12 q^{63} + 9 q^{64} + 3 q^{65} - 3 q^{66} - 27 q^{67} + 12 q^{68} - 6 q^{69} + 3 q^{70} - 9 q^{71} - 12 q^{72} + 51 q^{73} + 9 q^{74} + 3 q^{75} + 3 q^{77} - 33 q^{78} - 24 q^{79} + 3 q^{80} - 3 q^{81} + 3 q^{82} + 9 q^{83} + 3 q^{84} + 6 q^{85} - 21 q^{86} - 3 q^{87} + 3 q^{88} - 9 q^{89} - 18 q^{90} + 12 q^{91} + 6 q^{92} + 3 q^{93} - 21 q^{94} + 3 q^{96} + 12 q^{97} - 9 q^{98} - 15 q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 - 3 * q^3 + 9 * q^4 + 3 * q^5 + 3 * q^6 - 9 * q^7 - 9 * q^8 + 12 * q^9 - 3 * q^10 - 3 * q^11 - 3 * q^12 - 12 * q^13 + 9 * q^14 + 6 * q^15 + 9 * q^16 + 12 * q^17 - 12 * q^18 + 3 * q^20 + 3 * q^21 + 3 * q^22 + 6 * q^23 + 3 * q^24 + 12 * q^26 - 24 * q^27 - 9 * q^28 + 6 * q^29 - 6 * q^30 - 9 * q^31 - 9 * q^32 + 3 * q^33 - 12 * q^34 - 3 * q^35 + 12 * q^36 - 9 * q^37 + 33 * q^39 - 3 * q^40 - 3 * q^41 - 3 * q^42 + 21 * q^43 - 3 * q^44 + 18 * q^45 - 6 * q^46 + 21 * q^47 - 3 * q^48 + 9 * q^49 - 39 * q^51 - 12 * q^52 + 24 * q^54 + 24 * q^55 + 9 * q^56 - 6 * q^58 + 9 * q^59 + 6 * q^60 + 6 * q^61 + 9 * q^62 - 12 * q^63 + 9 * q^64 + 3 * q^65 - 3 * q^66 - 27 * q^67 + 12 * q^68 - 6 * q^69 + 3 * q^70 - 9 * q^71 - 12 * q^72 + 51 * q^73 + 9 * q^74 + 3 * q^75 + 3 * q^77 - 33 * q^78 - 24 * q^79 + 3 * q^80 - 3 * q^81 + 3 * q^82 + 9 * q^83 + 3 * q^84 + 6 * q^85 - 21 * q^86 - 3 * q^87 + 3 * q^88 - 9 * q^89 - 18 * q^90 + 12 * q^91 + 6 * q^92 + 3 * q^93 - 21 * q^94 + 3 * q^96 + 12 * q^97 - 9 * q^98 - 15 * q^99

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